Traffic Offloading and Wireless Edge Networks:
Theory and Novel Realizations
Leandros Tassiulas
Yale University
WiOpt,
Paris, May 2017.
A New Era in Wireless Networking
• Recent developments:
• Mobile data traffic growth, new services & advanced devices, 5G vision.
• Challenges for cellular networks:
• Accommodate the growing traffic.
• Support emerging 5G services.
• Traditional network expansion methods:
• Upgrading technology, acquiring new spectrum, deploying more cells, ...
... are costly and time-consuming solutions.
• Our approach:
• Explore methods that aim to fully utilize (i) existing spectrum allocations and
(ii) idle user-owned wireless infrastructure.
Outline
• Mobile data offloading.
• Use Wi-Fi capacity to serve cellular traffic.
• User Provided Networks (UPNs).
• Facilitate multi hop wireless access through exchange of wireless resources.
• Prototype realization based on mobile SDN.
• Resource exchange markets in networks.
• An Arrow-Debreu type formulation for networks.
Mobile Data Offloading
Offloading can be realized over femtocells or Wi-Fi access points.
• Goal: reduce network costs (OpEx) & accommodate more traffic.
• The wireless spectrum or the wired link are not owned by the operator.
Potential and Key Question
• Mobile network operators have adopted such solutions:
• AT&T had deployed 32,000 Wi-Fi hotspots by 2012.
• T-Mobile and other operators, collaborate with FON.
• Republic Wireless, Google Fi, etc.
• Offloading benefits depend on the availability of APs’.
• How to increase this availability?
• Our proposal for operators: lease idle user-owned Wi-Fi APs.
• Residential Wi-Fi APs are often underutilized.
• On-demand & low-cost network capacity expansion.
• Fully aligned with 5G design principles.
Mobile Data Offloading Markets
•
Related Publications:
• G. Iosifidis, L. Gao, J. Huang, L. Tassiulas, An Iterative Double Auction for
Mobile Data Offloading, IEEE WiOpt, 2013, (Best paper Award), IEEE/ACM
Trans. on Networking, 23(5), 2015.
• K. Poularakis, G. Iosifidis, L. Tassiulas, Deploying Carrier-grade WiFi:
Offload Traffic, Not Money, ACM Mobihoc, 2016.
• L. Gao, G. Iosifidis, J. Huang, L. Tassiulas, D. Li, Bargaining-Based Mobile
Data Offloading, IEEE JSAC, SI on 5G, 32(6), 2014.
• A. Apostolaras, G. Iosifidis, K. Chounos, T. Korakis, L. Tassiulas, A
Mechanism for Mobile Data Offloading to Wireless Mesh Networks, IEEE
Trans. on Wireless Comm., 15(9), 2016.
• K. Poularakis, G. Iosifidis, I. Pefkianakis, L. Tassiulas, Mobile Data
Offloading through Caching in Residential 802.11 Wireless Networks, IEEE
Trans. on Network Services & Management, 13(1), 2016.
Data Offloading Marketplace
• A set of network operators:
• Each operator owns many base stations.
• Each BS had different load.
• A set of access points:
• Each AP has different Internet capacity.
• AP owners have communication needs.
• A Broker
• Goal & Key questions:
• Efficiency: maximize BSs’ benefits, minimize APs’ costs.
• How much traffic from each BS should be offloaded to each AP?
• How much each AP owner should be reimbursed for serving this traffic?
• Technical Issues:
• Offloading Benefits are AP-specific and interdependent.
• Offloading Capacities of the APs are coupled.
Data Offloading Marketplace
• A set of network operators:
• Each operator owns many base stations.
• Each BS serves different amount of traffic.
• A set of access points:
• Each AP has different Internet capacity.
• AP owners have communication needs.
• A Broker
• Economic Issues:
• Multiple buyers & multiple sellers with conflicting goals.
• Information asymmetry about the needs.
• Solution approach:
• Use an auction to elicit hidden information.
• Traditional auctions, e.g., VCG and McAfee, cannot be used.
• Design a new auction algorithm.
G. Iosifidis, L. Gao, J. Huang, L. Tassiulas, A Double Auction Mechanism for Mobile Data
Offloading Markets, IEEE/ACM Trans. on Networking, vol. 23, no. 5, 2015.
Data Offloading Marketplace
• A set of network operators:
• Each operator owns many base stations.
• Each BS serves different amount of traffic.
• A set of access points:
• Each AP has different Internet capacity.
• AP owners have communication needs.
• A Broker
• Economic Issues:
• Multiple buyers & multiple sellers with conflicting goals.
• Information asymmetry about the needs.
• Solution approach:
• Use an auction to elicit hidden information.
• Traditional auctions, e.g., VCG and McAfee, cannot be used.
• Design a new auction algorithm.
G. Iosifidis, L. Gao, J. Huang, L. Tassiulas, A Double Auction Mechanism for Mobile Data
Offloading Markets, IEEE/ACM Trans. on Networking, vol. 23, no. 5, 2015.
Data Offloading Marketplace
• A set of network operators:
• Each operator owns many base stations.
• Each BS serves different amount of traffic.
• A set of access points:
• Each AP has different Internet capacity.
• AP owners have communication needs.
• A Broker
• Economic Issues:
• Multiple buyers & multiple sellers with conflicting goals.
• Information asymmetry about the needs.
• Solution approach:
• Use an auction to elicit hidden information.
• Traditional auctions, e.g., VCG and McAfee, cannot be used.
• Design a new auction algorithm.
G. Iosifidis, L. Gao, J. Huang, L. Tassiulas, A Double Auction Mechanism for Mobile Data
Offloading Markets, IEEE/ACM Trans. on Networking, vol. 23, no. 5, 2015.
Model
• A market of multiple BSs and multiple APs, studied for a period T :
• M, {1, ..., M}: the set of BSs; I, {1, ..., I}: the set of involved APs.
• Base station m:
• xm , {xm1 , ..., xmI }: offload request vector.
• Jm (xm ): offloading benefit.
• Access Point i:
• Ci : Internet access capacity.
• yi , {yi1 , ..., yiM }: offload admission vector.
• Vi (yi ): offloading cost.
• Broker’s objective: Efficiency Maximization
X
maximize
xm ,yi ,8m,8i
Jm (xm )
m2M
subject to (i)
(iii)
P
m2M
X
Vi (yi )
Efficiency
i2I
yim  Ci , 8i 2 I,
xmi = yim , 8m 2 M, i 2 I.
Capacity constraint
Feasibility
Iterative Double Auction – IDA
• An auction mechanism includes:
• An allocation rule & a pricing rule.
• Bidders’ Bidding Problems
• BS Bids: pm = (pmi : i = 1, . . . , I) .
Pm : maximize Jm (xm (pm ))
pmi
0,8i
hm (pm ),
for every BS m;
• AP Bids: ↵i = (↵im : m = 1, . . . , M) .
Pi : maximize
↵im
Vi (yi (↵i )) + li (↵i ),
0,8m
• Broker’s Allocation Problem
maximize
xm ,yi ,8m,8i
X X⇣
m2M i2I
subject to (i)
(ii)
P
m2M
pmi log xmi
for every AP i.
↵im 2 ⌘
yim
2
yim  Ci , 8i 2 I,
xmi = yim , 8m 2 M, i 2 I.
Iterative Double Auction – IDA
• The KKT conditions for the efficiency maximization problem:
(A1) :
(A3) :
@Jm (xm )
@Vi (yi )
= µmi , (A2) :
= µmi
@xmi
@yim
M
⇣X
⌘
yim Ci = 0, (A4) : xmi = yim ,
i ·
i
,
m=1
(A5) :
µmi · (yim
xmi ) = 0, (A6) : xmi , yim ,
i
0.
• The KKT conditions for the broker problem:
⇤
(B1) : xmi
=
pmi
µ⇤
⇤
, (B2) : yim
= mi
⇤
µmi
↵im
⇤
i
, (B3)
(B6) = (A3)
• If APs and BSs submit:
⇤
pmi = xmi
·
... the solutions coincide.
@Jm (xm⇤ )
1 @Vi (yi⇤ )
, ↵im = ⇤ ·
@xmi
yim
@yim
(A6)
Iterative Double Auction – IDA
• The KKT conditions for the efficiency maximization problem:
(A1) :
(A3) :
@Jm (xm )
@Vi (yi )
= µmi , (A2) :
= µmi
@xmi
@yim
M
⇣X
⌘
yim Ci = 0, (A4) : xmi = yim ,
i ·
i
,
m=1
(A5) :
µmi · (yim
xmi ) = 0, (A6) : xmi , yim ,
i
0.
• The KKT conditions for the broker problem:
⇤
(B1) : xmi
=
pmi
µ⇤
⇤
, (B2) : yim
= mi
⇤
µmi
↵im
⇤
i
, (B3)
(B6) = (A3)
• If APs and BSs submit:
⇤
pmi = xmi
·
... the solutions coincide.
@Jm (xm⇤ )
1 @Vi (yi⇤ )
, ↵im = ⇤ ·
@xmi
yim
@yim
(A6)
Iterative Double Auction – IDA
• The payment and reimbursement rules we employ are:
300
pmi , m = 1, . . . , M
i=1
yim (
200
150
100
50
i
µmi ), i = 1, . . . , I
0
0
m=1
Fig. 3.
20
40
60
80
Step − t
100
120
140
Evolution of social welfare produced by the IDA.
0.4
0.2
0
Gap y − x
li (↵i ) =
M
X
taking b
work. F
price-an
it is cha
the alg
implem
to APs
execute
250
Social Welfare − SW
hm (pm ) =
I
X
−0.2
BS 1, AP 1: y11 −x11
BS 1, AP 2: y21−x12
−0.4
BS 2, AP 1: y −x
12
−0.6
21
BS 2, AP 2: y22−x22
−0.8
−1
−1.2
0
20
40
60
80
100
120
Step − t
Fig. 4.
Evolution of the gap between requested (x) and admitted data (y).
⇢11 = 0.74. Finally, the payments of the BSs 1, 2 and 5 are
p11 = 7.3, p21 = 6.29, and p51 = 6.63, respectively. Notice
that BS 5 pays less than BS 1 although it offloads more data
[1] Cisco
Forec
[2] Bloo
[3] Femt
[4] AT&
Addi
[5] BT W
Custo
[6] Cisco
[7] Repu
[8] Spec
[9] R. B
Bilat
[10] R.
Econ
[11] P. M
Prici
[12] D.
Netw
1451
[13] F. P
Netw
of O
[14] L. J
[15] K. L
How
[16] N. R
Effic
[17] Info
Iterative Double Auction – IDA
1
BS2
BS1
BROKER
1
Broker announces
pricing signals
(Lagrange Multipliers)
AP1
AP2
AP3
The broker announces the pricing signals
i , µmi , i 2 I, m 2 M.
Iterative Double Auction – IDA
Each BS finds its
currently optimal bid
vector
1
2
2
BS2
BS1
BROKER
AP1
AP2
Each AP find its
currently optimal bid
vector
2
AP3
The broker announces the pricing signals
i , µmi , i 2 I, m 2 M.
Each AP i and BS m updates its bids
using the new Lagrange multipliers.
Iterative Double Auction – IDA
1
3
Each BS sends its
bids to the broker
2
BS2
BS1
3
BROKER
AP1
AP3
AP2
3
Each AP sends its
bids to the broker
The broker announces the pricing signals
i , µmi , i 2 I, m 2 M.
Each AP i and BS m updates its bids
using the new Lagrange multipliers.
APs and BSs send their bids to the
broker.
Iterative Double Auction – IDA
BS
BS
1
2
BROKER
The Broker updates
the Lagrange
Multipliers
4
AP1
AP2
The broker announces the pricing signals
i , µmi , i 2 I, m 2 M.
Each AP i and BS m updates its bids
using the new Lagrange multipliers.
3
APs and BSs send their bids to the
broker.
4
The broker updates the pricing signals
µmi , i 2 I, m 2 M, using a gradient
update.
AP3
i,
Iterative Double Auction – IDA
BS
BS
1
2
BROKER
The Broker updates
the Lagrange
Multipliers
4
AP1
AP2
The broker announces the pricing signals
i , µmi , i 2 I, m 2 M.
Each AP i and BS m updates its bids
using the new Lagrange multipliers.
3
APs and BSs send their bids to the
broker.
4
The broker updates the pricing signals
i 2 I, µm , m 2 M, using a gradient
update method.
5
The above steps are executed iteratively
until convergence: demands match
offerings.
AP3
i,
Summary
• A mobile data offloading market for leasing idle capacity.
• A new auction algorithm that achieves the optimal solution.
• No need to know offloading needs and cost functions.
• Can use a detailed network modeling approach.
• Other market models are also important to explore.
• Example: MNO reimburses its subscribers to open their APs.
• Caching-at-the-edge solutions employing user-owned APs.
• Intel’s 2011 experiments showed 40% reduction in backhaul traffic.
L. Gao, G. Iosifidis, J. Huang, L. Tassiulas, D. Li, Bargaining-based Mobile Data Offloading,
IEEE JSAC, SI on 5G, 32(6), 2014.
K. Poularakis, G. Iosifidis, et al, Mobile Data Offloading through Caching in Residential 802.11
Wireless Networks, IEEE Trans. on Network Services & Management, 2016.
User Provided Networks (UPNs)
• Related publications:
• G. Iosifidis, L. Gao, J. Huang, L. Tassiulas, Enabling Crowdsourced Mobile Internet
Access, IEEE Infocom, 2014, cond. accepted in IEEE/ACM ToN 2016.
• G. Iosifidis, L. Gao, J. Huang, L. Tassiulas, Incentive Mechanisms for User-provided
Networks, IEEE Communications Magazine, 52 (9), Sep., 2014.
• L. Gao, G. Iosifidis, J. Huang, L. Tassiulas, Hybrid Data Pricing for Network-Assisted
User-Provided Connectivity, IEEE Infocom, 2014.
• D. Syrivelis, G. Iosifidis, D. Delimbasis, K. Chounos, T. Korakis, L. Tassiulas, Bits and
Coins: Supporting Collaborative Consumption of Mobile Internet, IEEE Infocom, 2015.
• D. Giatsios, G. Iosifidis, and L. Tassiulas, Mobile edge-Networking Architectures and
Control Policies for 5G Communication Systems, WiOpt, 2016.
User Provided Networks
Congested
High-Performance
WiFi
Cell
WiFi/Bluetooth
Malfunctioned
Cell
WiFi/Bluetooth
• Indicative Applications:
• Provide infrastructure connectivity to devices with no access.
• Overcome poor coverage through smart relaying.
• Support throughput-hungry services.
• Alleviate congestion problems or temporal malfunctions of the infrastructure.
• Innovative startups have already presented such solutions.
• Question: Can we find an optimal operation policy?
• How to aggregate and share the users’ network resources in an efficient and
fair fashion, such that users have enough incentives to participate?
G. Iosifidis, L. Gao, J. Huang, L. Tassiulas, Enabling Crowdsourced Mobile Internet Access,
IEEE Infocom, 2014, cond. accepted in IEEE/ACM ToN.
User Provided Networks
Congested
High-Performance
WiFi
Cell
WiFi/Bluetooth
Malfunctioned
Cell
WiFi/Bluetooth
• Indicative Applications:
• Provide infrastructure connectivity to devices with no access.
• Overcome poor coverage through smart relaying.
• Support throughput-hungry services.
• Alleviate congestion problems or temporal malfunctions of the infrastructure.
• Innovative startups have already presented such solutions.
• Question: Can we find an optimal operation policy?
• How to aggregate and share the users’ network resources in an efficient and
fair fashion, such that users have enough incentives to participate?
G. Iosifidis, L. Gao, J. Huang, L. Tassiulas, Enabling Crowdsourced Mobile Internet Access,
IEEE Infocom, 2014, cond. accepted in IEEE/ACM ToN.
Proposed Solution
• A mechanism based on the Nash bargraining solution + virtual currency.
• Users are modeled through payoff functions.
• Utility from consuming data, energy cost and monetary cost for serving data,
virtual currency benefits.
• Efficiency and Fairness are addressed by the Nash Bargaining Solution.
• Pareto optimal.
• Takes into account the standalone operation of each node.
• Self-enforcing, hence users agree to apply the policy.
• Virtual Currency solves the double coincidence of needs and wants
problem.
• Decentralized implementation is possible if necessary.
• Dual decomposition of a convex optimization problem (the NBS problem).
Model
• A directed network G = (N , E) that we study for a period T .
• In(i): parent nodes of i, Out(i): child nodes of i.
• Each node n 2 N can initiate a data session (n).
• Cij : capacity of (i, j) 2 E , C0i : Internet capacity of i 2 N .
(n)
• xij : bytes transferred over link (i, j), for commodity (n).
(n)
• yi : bytes downloaded by node i, for commodity (n).
• Ui (ri ): utility function modeling his communication needs, where
(i)
ri = yi
+
X
(i)
j2In(i)
xji
• Vi (ei ): energy consumption aversion function, where ei is the total
consumed energy in T :
X
X (n)
X
X (n)
X (n)
ei =
eijs
xij +
ejir
xji + e0i
yi .
j2Out(i)
n2N
j2In(i)
n2N
• pi
0: Internet access cost per byte.
• The overall payoff Ji (·) is defined as:
Ji (x, y) = Ui (ri )
Vi (ei )
pi
n2N
X
n2N
(n)
yi
Problem Formulation
• Standalone performance: no relaying to/from others.
(i)
max Ji (yi )
(i)
yi C0i
Benchmark (minimum) performance Jis = Ji (yi
⇤ (i)
).
• Virtual Coins system:
• Di : the initial coin budget of each user i 2 N .
• Hi (·): the coins valuation function of user i (linear).
(n)
• zij : coins paid by j to i, for commodity (n), with (i, j) 2 E.
• Each user receives
> 0 coins for his participation in each round.
• Total budget of K coins in the system (upper bound).
• The payoff of each user includes now the coin budget:
JiG (x, y, z) = Ji (x, y) + Hi (z, Di + )
Bargaining Problem
• The bargaining equilibrium can be derived by the solution of the
following convex problem.
max
x,y,z
s.t.
X
X
log JiG (x, x, y)
(n)
xji
(n)
+ yi
=
j2In(i)
X
n2N
(n)
zji
n2N j2In(i)
X X
(n)
X
n2N
(n)
zij
n2N j2Out(i)
JiG (x, x, y)
(n)
Hi (z, Di )
xij , 8 i, n 2 N , i 6= n,
 Cij , 8 (i, j) 2 E,
X X
xij
X
j2Out(i)
(n)
xij
Jis
i2N
(n)
0, yi
(n)
yi
 C0i , 8 i 2 N
 Di + , 8i 2 N
Jis + Hi (z, Di ), 8 i 2 N
(n)
0, 0  zij
 K , 8 i, j, n 2 N
(1)
(2)
(3)
(4)
(5)
• where eq. (4) ensures that each user will receive a payoff at least equal
to his standalone performance.
User Provided Networks
• Question: Can we implement such systems in practice?
• Requirements:
• Independent of the physical layer.
• Highly adaptive to changing network conditions and users’ needs.
User Provided Networks
• Question: Can we implement such systems in practice?
• Requirements:
• Independent of the physical layer.
• Highly adaptive to changing network conditions and users’ needs.
CoNeS: Collaborative Network Sharing System
• Basic components:
• SDN-enhanced mobile devices: implement a programmable packet
forwarding datapath.
• Cloud service: monitors the nodes, and devises the policy.
D. Syrivelis, G. Iosifidis, D. Delimpasis, K. Chounos, T. Korakis, L. Tassiulas, Bits & Coins:
Supporting Collaborative Consumption of Mobile Internet, IEEE Infocom, 2015.
CoNeS: Collaborative Network Sharing System
Network Data Collection
Statistics,
Demands,
Resources,
Discovery
CDE
Decision
Graph
SMDP Service
MBaaS Platform
WiFi
ISCD Service
Downloading /
Uploading Data
D2D links
SDN
Data
Path
Internet
Decision Graph Derivation
SDN
Control
Plane
Decision
Graph
Client
Statistics
& Demands
1
D2D data
exchange
D2D links
Client
Relay/Client
2
3G/4G
Gateway
Client
Device Characteristics
· Internet access capacity
· Internet access cost
· D2D links capacity
· Battery energy
1
• 1: Every node executes neighbor discovery.
• 2: Forwards to the cloud the network information (D2D links capacity), its
resource availability (battery, Internet throughput), and its demand.
CoNeS: Collaborative Network Sharing System
3
Network Data Collection
Internet
Statistics,
Demands,
Resources,
Discovery
CDE
4
Decision
Graph
SMDP Service
MBaaS Platform
WiFi
ISCD Service
3G/4G
Downloading /
Uploading Data
D2D links
SDN
Data
Path
3
Decision Graph Derivation
SDN
Control
Plane
Decision
Graph
4
Client
Statistics
& Demands
D2D data
exchange
D2D links
Client
Relay/Client
Client
Device Characteristics
· Internet access capacity
· Internet access cost
· D2D links capacity
· Battery energy
Gateway
• 3: The CDE collects the information; derives the servicing policy.
• 4: The decision graph is communicated to the nodes of the swarm.
Steps 1 - 4 are executed periodically.
CoNeS: Collaborative Network Sharing System
3
Network Data Collection
Internet
Statistics,
Demands,
Resources,
Discovery
CDE
4
Decision
Graph
SMDP Service
MBaaS Platform
WiFi
ISCD Service
3G/4G
Downloading /
Uploading Data
D2D links
SDN
Data
Path
3
Decision Graph Derivation
SDN
Control
Plane
Decision
Graph
4
Client
Statistics
& Demands
D2D data
exchange
D2D links
Client
Relay/Client
Client
Device Characteristics
· Internet access capacity
· Internet access cost
· D2D links capacity
· Battery energy
Gateway
• 3: The CDE collects the information; derives the servicing policy.
• 4: The decision graph is communicated to the nodes of the swarm.
Steps 1 - 4 are executed periodically.
x
x
x
Inside the Node
VPN Default
Internet Gateway
Tunnel
ICSD
dcs
cfs
Local IP Stack
OpenFlow
API
Mobile Node SMD
(Linux Kernel)
Virtual
Ethernet
Local Port
OVS - Switch
HTB1
Queues
HTB2
Queues
Port 1
Port 2
Port N
HTBN
Queues
Bluetooth Phy
WiFi Phy
LTE Phy
• Open vSwitch datapath:
• Remotely configured, controls all network interfaces.
• Internet Connection Sharing Daemon (ICSD):
• Runs a discovery protocol & reports to CDE; gets & applies updates.
Performance Evaluation
• How often should the devices send status to the cloud?
• How fast is it possible to reconfigure the network?
• How much is the delay, bandwidth and energy consumption overhead?
Performance Evaluation
• How often should the devices send status to the cloud?
• How fast is it possible to reconfigure the network?
• How much is the delay, bandwidth and energy consumption overhead?
Performance Evaluation
• How often should the devices send status to the cloud?
• How fast is it possible to reconfigure the network?
• How much is the delay, bandwidth and energy consumption overhead?
Experimental Setup
• Embedded Nodes (single-board computers):
• Intel Atom CPU, 1Gbyte RAM,
• 802.11n WiFi (ad hoc mode), 100Mbit cable Ethernet interface.
• Real-time power consumption measurement.
• The cloud service is deployed at the NITOS cluster.
Experiments Findings
Internet
Internet
1
Gateway
Gateway
2
(1)
(2)
Client 3
• Status updates:
• 3 sec is optimal, 2.5% energy consumption, no additional delay. More
frequent updates double energy consumption.
• SDN Overheads:
• No important energy consumption or computation overheads (2%).
• Network reconfiguration:
• Gateway switching every 20 sec increases delay 24%, and energy
consumption 15%
Service & Resource Exchange over Networks
• Basic features of the system:
• Each node has some amount of spare resource.
• Nodes are complementary in terms of resource types or resource
availability.
• Their cooperation is constrained by a graph.
• Unsaturated demand.
• Indifferent in neighbors’ resources.
Service & Resource Exchange over Networks
• Various decentralized technological networks:
• Peer-to-peer file sharing overlays.
• Wireless mesh networks, Wi-Fi communities, Mobile Internet sharing.
• Renewable energy sharing in smart grid.
• Sharing economy platforms:
• Online bartering: swap.com, neighborgoods.net, etc.
• Food sharing, favor exchanging, risk sharing, etc.
• More examples: http://www.collaborativeconsumption.com/
L. Georgiadis, G. Iosifidis, L. Tassiulas, ”Exchange of Services in Networks: Competition,
Cooperation, and Fairness”, ACM Sigmetrics, 2015.
Model
• An undirected connected graph G = (N , E).
• Set of allocations:
D = d = (dij )(i,j)2E : dij
0,
X
j2Ni
dij = Di }
• Set of feasible received resource vectors:
R = r = (ri )i2N : ri =
X
j2Ni
dji , i 2 N , d 2 D ,
• Individual node’s objective: to maximize his received resource ri , i 2 N .
• Exchange ratio vector:
⇢i =
ri
ri
, ⇢ = (⇢i =
: i 2 N)
Di
Di
Central Coordination Fair Allocations
• Question: Which is a sensible allocation?
• Ideal allocation: ri = Di , 8 i 2 N , i.e., ⇢i = 1
• Else: balance the exchange ratios as much as possible.
• Lexicographically optimal (Max-min fair) vector of exchange ratios ⇢.
• There is a unique lex-optimal vector of exchange ratios ⇢⇤ ⌫ ⇢.
• Set R of received resource vectors is compact and convex, and ⇢i = ri /Di .
• Also interested in the allocations d ⇤ that yield ⇢⇤ .
• While ⇢⇤ is unique, there are many allocations d ⇤ .
• Question: What are the main properties of ⇢⇤ .
Properties of ⇢⇤
• There is a unique ⇢⇤ and one or more d ⇤ 2 D, with properties:
• Nodes are partitioned in distinct exchange ratio sets
L1 , L2 , . . . , L7 .
• K = 7 depends on G and {Di } .
• L7 nodes work only with L1 nodes, and so on.
• It holds: l1 · l7 = l2 · l6 = . . . = 1.
• Topology: Lk is independent in the induced graph
GQk = (Qk , EQk ), k = 1, . . . , 3, where
1
Qk = N [km=1
(Lm [ LK m+1 ).
⇤
• Topology: L⇤
K k +1 = NQk Lk , k = 1, ...., 3.
• Theorem: If an allocation policy satisfies the above properties, then it is
lex-optimal.
Stability wrt Trade
• A Competitive Market.
• Every node i 2 N determines independently his allocation policy dij
j2Ni
• Objective: maximize
P
j
dji , or, equivalently, the ratio ⇢i = ri /Di .
• Ratio ⇢i can be interpreted as the price that node i sells his resource.
• An allocation d ⇤ is an exchange equilibrium iff 8i 2 N :
• dji = dij · ⇢i , 8 j 2 Ni .
• if dji > 0 for some j 2 Ni , then ⇢j = mink 2N ⇢k .
i
• Does an exchange equilibrium exist?
• General Equilibrium theory: equilibrium exists under some mild conditions.
• Existence conditions do not apply in the proposed model:
• Not all nodes are endowed with non-zero quantities.
• Prices are not given exogenously; instead, they are indirectly determined by
the nodes’ decisions.
K. J. Arrow, G. Debreu, ”Existence of and Equilibrium for a Competitive Economy”,
Econometrica 22(3), 1954.
Stability wrt Trade
Theorem.
1
There is a lex-optimal allocation d ⇤ under which every node i 2 N gives
resource to its neighbors in proportion to what it gets from them, i.e.,
dji⇤
r⇤
= i = ⇢⇤i , 8 j 2 Di .
⇤
dij
Di
2
The neighbors not receiving resource from i have higher ratio ⇢j , i.e.,
⇢⇤j
3
1
, 8 j 2 Ni
⇢⇤i
Di .
If the allocation satisfies the above conditions, then it is lex-optimal.
• Interpretation:
• There is a lex-optimal allocation where every node i 2 N serves its
neighbors with the same exchange ratio (or, not at all).
• Any possible exchange equilibrium is also a lex-optimal allocation.
The competitive interactions of users embedded in a graph yield the
same allocation point a central designer would have selected.
Stability wrt Coalitions
• Assume that subsets of nodes may decide to exchange only among
themselves.
• NTU Coalitional Service Exchange game:
• Played over the graph G = (N , E), by N players.
P
• Each node i has strategy di = dij : j 2 Ni ,
j dij = Di , and utility ri .
• (Strong) Stability Definition:
• An allocation d (and the resource vector r) is called strongly stable if
bS on the induced subgraph GS = (S, ES ),
8S ✓ N , there is no allocation d
such that b
ri
ri 8i 2 S, and b
rj > rj for at least one node j 2 S.
• Theorem: The only (strongly) stable allocations with respect to
coalitions are those with lexicographically optimal resource vectors r ⇤ .
• Hence, the solution of the graph-constrained coalitional game has the above
topological and price properties.
Dynamic Interactions
• How can the nodes find this equilibrium?
• Dynamic setup:
• Each node i creates ”service token” (e.g., relay opportunity) according to a
Poisson process with rate
i
= Di .
• Every token is allocated to the neighbor with the lowest exchange rate (i.e.,
larger reciprocation).
• Decentralized and asynchronous best response under limited information.
• Extensive numerical results show that the system converges to the
unique vector of exchange ratios ⇢⇤ .
• Previous works showed convergence numerically for similar models, or
even proved it under certain conditions.
F. Wu, et al, Proportional Response Dynamics Leads to Market Equilibrium, ACM STOC’ 07
B. Birnbaum, et al., Distributed Algorithms via Gradient Descent for Fisher Markets, EC’ 11
R. Cole, et al., Fast-Converging Tatonnement Algorithms for One-Time and Ongoing Market
Problems, ACM STOC’ 08.
Overview
• The above models are motivated by the sharing economy.
• MNOs and start ups are already employing similar ideas.
• Novel opportunities for fundamental and experimentation-driven research.
• What will be the Uber, or Airbnb model for wireless networks?
• Mobile data offloading (leased) architectures.
• Leverage dormant user-owned capacity.
• Designed an efficient market mechanism.
• Move towards carrier-grade offloading solutions.
• UPN collaborative systems.
• Bottom-up networking solutions.
• Designed a resource allocation policy.
• Implemented a prototype system.
• Network resource exchange economies.
• Decentralized and dynamic bartering markets.
• Characterized the structure and efficiency of equilibriums.